Leaking Cylindrical Tank—Continued When friction and contraction of the water at the hole are taken into account, the model in Problem 11 becomes where 0 < c < 1. How long will it take the tank in Problem 11(b) to empty if c = 0.6? See Problem 13 in Exercises 1.3.
(reference problem 13 in exercise 1.3)
Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to is an empirical constant. Determine a differential equation for the height h of water at time t for the cubical tank shown in Figure 1.3.12. The radius of the hole is 2 in., and g =32 ft/s2.
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